Chris James Rose1,2, Penny Louise Hubbard1,2,
Caleb Roberts1,2, Simon S. Young3, Josephine H. Naish1,2,
Geoffrey J. Parker1,2
1The University of
Manchester Biomedical Imaging Institute, The University of Manchester,
Manchester, Greater Manchester, United Kingdom; 2Manchester
Academic Health Science Centre, The University of Manchester, Manchester,
Greater Manchester, United Kingdom; 3AstraZeneca R&D
Charnwood, Loughborough, Leicestershire, United Kingdom
Voxel-wise measurements of ventilation-to-perfusion ratio (V/Q) in the lung can be made using oxygen-enhanced MRI (OE-MRI). Patients are dynamically imaged as they switch from breathing medical air to an elevated concentration of oxygen. The change in partial pressure of oxygen over time is modelled in terms of three parameters, v, q, and λB. We consider fitting this model to data and study the topology of the sum of squared differences (SSD) function. We demonstrate a valley in the SSD function of optimal v and q values satisfying v/q=V/Q, and show that v and q should not be interpreted independently.